Question: Solve for $x$ and $y$ using elimination. ${-6x-3y = -51}$ ${5x+3y = 47}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-6x-3y = -51}\thinspace$ to find $y$ ${-6}{(4)}{ - 3y = -51}$ $-24-3y = -51$ $-24{+24} - 3y = -51{+24}$ $-3y = -27$ $\dfrac{-3y}{{-3}} = \dfrac{-27}{{-3}}$ ${y = 9}$ You can also plug ${x = 4}$ into $\thinspace {5x+3y = 47}\thinspace$ and get the same answer for $y$ : ${5}{(4)}{ + 3y = 47}$ ${y = 9}$